Bright and dark solitons: Quasiperiodicity, mode-locking, and chaos under periodic forcing

Electron acoustic waves (EAWs) in a two-electron-temperature plasma, where the hot electron population follows a generalized r, q distribution, play a crucial role in understanding nonlinear electrostatic phenomena—a topic of significant importance in both laboratory and space plasmas. Using the reductive perturbation method, we derive the Kadomtsev–Petviashvili (KP) equation to describe the nonlinear evolution of small-amplitude EAWs in the complex plasma environment. Our analysis reveals that the system supports both bright (compressive) and dark (rarefactive) solitons, with their existence and structure susceptible to the plasma parameters and spectral indices. To explore external influences, we introduce an external periodic force (EPF) and perform a nonlinear dynamical analysis using bifurcation diagrams, Poincaré maps, fast Fourier transforms, and Lyapunov exponents. Our results reveal that an EPF profoundly alters system behavior at low frequencies; the system exhibits stiffness, transitions to quasiperiodicity, and eventually becomes chaotic, as confirmed by a positive Lyapunov exponent. Resonant dynamics, including mode-locking, are identified, showing transitions from island-chain structures to periodic points and, finally, to smooth quasiperiodic loops in the Poincaré section. This study provides the first detailed investigation of EPF-induced nonlinear dynamics in KP-modeled EAWs with r,q-distributed electrons, offering insights into mode-locking, bifurcation cascades, and chaos. These findings have significant implications for understanding energy transport in laboratory and space plasmas.